Problem: The decimal representation of a fraction ends in $0.\overline{3}$. When the decimal is changed to a common fraction and reduced to lowest terms, what is the denominator of the fraction?
Answer: Let $S = 0.\overline{3}$. Then $10S = 3.\overline{3}$. Subtracting the second equation from the first we obtain $9S = 3$, so $S = \frac13$. The desired denominator is $\boxed{3}$.